What is it we expect students to learn? Identifying Essential Standards
Grade Level: 11-12 Grade
Subject : Precalculus
1. Standard/
Description
Simplify and perform
operations with
exponents, radicals and
rational functions
Team Members: T. Knowles, T. Clement, J. Kurz, C.George
2. Evidence of Proficiency
Simplify:
3
a) √81
5
b) √64𝑥 12 𝑦 6
3
c) 𝑦 5 √𝑦
d)
3. Prior Skills
Needed
4. Common
Summative
Assessment`
1. Exponent rules
Chapter 1 Test
2. Perform operations on Chapter 3 test
fractions
3. Prime factoring to
Semester 1 final exam
break down radicals
5. When
Taught?
AugustOctober
5𝑥 −4 𝑦 2
5−2 𝑥 2 𝑦 8
e)
5
ab
4b
 2

2
a b a b
ab
f)
Solve:
3x  4  2  x
Solve and graph linear,
absolute value and
radical functions
Solve:
2
3
4
 2

5x  5 x 1 x 1
x 1  5  8
b)
x5  x2  3
c)
d) 3x  1  4  1
a)
e)
f)
2x  3  9
3  1  2x  3
1. Understand the x- and
y- axis system and be
able to plot points.
2. Calculate the slope of
a line.
3. Graph a line using the
slope-intercept
method.
4. Absolute value as the
distance from zero.
5. Understand that
inequalities have a
range of answers.
Chapter 1 test
Chapters 2 test
Semester 1 final exam
September
October
What is it we expect students to learn? Identifying Essential Standards
Solve and graph
quadratic functionsusing multiple methods
Solve polynomial,
exponential and
logarithmic functions
and identify properties
(zeros, asymptotes,
extrema) of each.
1. Graph the quadratic function
𝑦 = (𝑥 − 2)2 + 4
2. Solve 0 = 𝑥 2 − 𝑥 − 6 by ALL
of the following methods:
complete the square,
factoring, and quadratic
formula.
Identify the zeros, max and
mins of a quadratic function.
Use the function
f ( x)  x  4 x  32
2
1. Complete the square and find
the vertex form of the
function (2pts)
2. Graph the function, labeling
all important points. (4pts)
3. Identify: (9pts)
a. Vertex
b. Is the vertex a max or
a min?
c. Axis of Symmetry
domain
d. Range
e. Intervals where the
function is increasing
f. Intervals where the
function is decreasing
g. X-intercept & Y-intercepts
4. List the translations that were
performed on the function
g(x)=x2 to achieve the graph of
f(x) (2pts)
5. Identify all asymptotes and
𝑥 2 −𝑥−6
holes in 𝑦 = 𝑥 2 +𝑥−12
1. Shape of a quadratic
function
2. Basic factoring skills.
3. Understand the x- and
y- axis system and be
able to plot points
Chapter 2 test
Chapter 3 test
Chapter 4 test
Semester 1 Final exam
October
November
N/A
Chapter 2 test
Chapter 3 test
Chapter 4 test
Semester 1 Final Exam
OctoberDecember
What is it we expect students to learn? Identifying Essential Standards
Evaluate trig function
values of any angle in
both degrees and
radians.
1. Convert any angle between
radians and degrees
2. Evaluate:
𝜋
sin 45° + cos − 𝑐𝑠𝑐 2 (60°)
2
1. Basic understanding
of degree angle
measure
2. 30-60-90 reference
triangle
3. 45-45-90 reference
triangle
Chapter 5 Test
Cum Test ch5-7
Solve trigonometric
equations
Find the value of each of the other
five trigonometric functions for an
angle, Ø given the information
indicated.
−4
𝑡𝑎𝑛∅ =
𝑎𝑛𝑑 𝑠𝑖𝑛∅ < 0
3

Chapter 6 test
Chapter 7 test
Cum Test ch5-7
Semester 2 Final Exam
January-February
Chapter 6 test
Chapter 7 test
Cum Test ch5-7
Semester 2 Final Exam
February


Solve trig equations
a.
b.
c.
d.
Apply trig functions to
model real world
problems
Basic understanding
of degree angle
measure
30-60-90 reference
triangle
45-45-90 reference
triangle
January
Semester 2 Final exam
√3
𝑠𝑖𝑛𝑥 = 2
𝑠𝑖𝑛2 𝑥 − 2𝑠𝑖𝑛𝑥 = 0
∅
𝑠𝑖𝑛 2 − 2 = 1
2𝑠𝑖𝑛2 𝑥 + 5 cos 𝑥 + 1 =
0 , 0 ≤ 𝑥 < 2𝜋
1. Find the radian measure of a
central angle opposite an arc
of 10 cm long on a circle of
radius 3.5cm
2. Linear and angular velocity
3. Apply a trig function
regression given data that
follows a cyclic pattern
4. What are the amplitude and
period of the function?
𝜋
𝑦 = 5sin 4 (𝑥 − 8)
N/A
What is it we expect students to learn? Identifying Essential Standards
Solve systems of
equations graphically
and by substitution,
elimination,
matrices/determinants.
Solve each of the following
systems using ALL of the following
methods:
a. Substitution
b. Elimination
c. Gauss-Jordan
Elimination
d. Cramer’s Rule
e. Inverse Matrices
Ex:
2𝑥 + 5𝑦 = −34
−3𝑥 + 2𝑦 = −44
Ex:
3𝑥 + 4𝑦 + 2𝑧 = 3
5𝑥 − 2𝑦 − 13𝑧 = 3
4𝑥 + 3𝑦 − 3𝑧 = 6
1. Understand the x- and
y- axis system and be
able to plot points.
2. Be able to calculate a
Least Common
Multiple.
3. Distributive Property.
4. Replace a variable
with an algebraic
expression.
Chapter 2 test
Chapter 8 Test
Chapter 9 test
Semester 2 final Exam
September
March
April